Question 1031114: Out of 2000 students who attend a certain high school, 1400 students own cell phones, 1000 own a tablet, and 800 have both. Suppose a student is randomly selected. Create a Venn diagram model. I already tried it but I can't figure this out because the addend of the three numbers is more than 2000 and my teacher didn't explain it thoroughly. Please help me, thank you.
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Out of 2000 students who attend a certain high school, 1400 students own cell phones, 1000 own a tablet, and 800 have both. Suppose a student is randomly selected. Create a Venn diagram model. I already tried it but I can't figure this out because the addend of the three numbers is more than 2000
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Draw 2 intersecting circles inside a rectangle.
Put 800 in the intersection (this is an important 1at step).
Label one of the circles "tablet" and put 1000-800 = 200
in the circle but not in the intersection.
Label the other circle "cell phone" and put 1400-800 = 600 in
the circle but not in the intersection.
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The total number in the circles is now 200 + 800 + 600 = 1600
That means there are 400 in the rectangle but not in either
of the circles---those do not have a tablet and do not have a cell phone.
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Cheers,
Stan H.
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Answer by ikleyn(52833)  (Show Source):
You can put this solution on YOUR website! .
Out of 2000 students who attend a certain high school, 1400 students own cell phones, 1000 own a tablet, and 800 have both.
Suppose a student is randomly selected. Create a Venn diagram model. I already tried it but I can't figure this out
because the addend of the three numbers is more than 2000 and my teacher didn't explain it thoroughly. Please help me, thank you.
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Let S be the full set of 2000 students in the high school,
C be the set of those who own cell phones (1400 students), and
T be the set of those who own tablets (1000 students).
The intersection CT of C and T counts 800 students.
600 students of C (600 = 1400-800), who are not in the intersection, have only cell phones an have no tablets.
200 students of T (200 = 1000-800), who are not in the intersection, have only tablets and have no cell phones.
The number of those who has cell phone OR tablet is 800 + 200 + 600 = 1600.
The remaining 400 students (400 = 2000 - 1600) have neither cell phone nor tablet.
Now draw a rectangle, which will represent 2000 students of the school.
Inside the rectangle, draw two smaller intersecting circles, representing the sets C and T.
The intersection of the two circles represents the set CT.
The exterior of the two circles inside the rectangle represents those students who has neither cell phone nor tablet.
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